In a recent paper [Phys. Rev. D 72, 085006 (2005)], Brandt et al. deduced the thermal operator representation for a thermal $N$-point amplitude, both in the imaginary-time and real-time formalisms. In the case when a chemical potential present, however, the representation is not as simple as in the case with vanishing chemical potential. We propose a much simpler and transparent representation for the case of nonzero chemical potential.

We discuss the possibility to probe leptonic mixing parameters at high-energy neutrino telescopes in a model-independent way, using astrophysical neutron and pion sources. In particular we show how the octant of the 2-3 mixing angle might be determined independently of prior knowledge of the source, even when current uncertainties on the other mixing parameters are included. We also argue that nontrivial neutrino oscillation effects should be taken into account when using high-energy flavor ratios for astrophysical diagnostics.

For supersymmetric spacetimes in 11 dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and sufficient conditions are comprised of algebraic relationships, linear in the spinorial components, between the spinorial components and their first derivatives, and the components of the spin connection and four-form. The integrability conditions for the Killing spinor equation are also analyzed in detail, to determine which components of the field equations are implied by arbitrary additional supersymmetries and the four-form Bianchi identity. This provides a complete formalism for the systematic and exhaustive investigation of all spacetimes with extended null supersymmetry in 11 dimensions. The formalism is employed to show that the general bosonic solution of 11 dimensional supergravity admitting a $G_2$ structure defined by four Killing spinors is either locally the direct product of ${\mathbb{R}}^{1,3}$ with a seven-manifold of $G_2$ holonomy, or locally the Freund-Rubin direct product of ${\mathrm{AdS}}_4$ with a seven-manifold of weak $G_2$ holonomy. In addition, all supersymmetric spacetimes admitting a $(G_2⋉{\mathbb{R}}^7)\times {\mathbb{R}}^2$ structure are classified.

We classify all the structure groups which arise as subgroups of the isotropy group, $(\mathrm{Spin}(7)⋉{\mathbb{R}}^8)\times \mathbb{R}$, of a single null Killing spinor in 11 dimensions. We construct the spaces of spinors fixed by these groups. We determine the conditions under which structure subgroups of the maximal null structure group $(\mathrm{Spin}(7)⋉{\mathbb{R}}^8)\times \mathbb{R}$ may also be embedded in $\mathrm{SU}(5)$, and hence the conditions under which a supersymmetric spacetime admits only null, or both timelike and null, Killing spinors. We discuss how this purely algebraic material will facilitate the direct analysis of the Killing spinor equation of 11 dimensional supergravity, and the classification of supersymmetric spacetimes therein.

We demonstrate that a two-brane system with a bulk scalar field driving power-law inflation on the branes has an instability in the radion. We solve for the resulting trajectory of the brane, and find that the instability can lead to collision. Brane quantities such as the scale factor are shown to be regular at this collision. In addition we describe the system using a low-energy expansion. The low-energy expansion accurately reproduces the known exact solution, but also identifies an alternative solution for the bulk metric and brane trajectory.

In this paper, charged black holes in general relativity coupled to Born-Infeld electrodynamics are studied as gravitational lenses. The positions and magnifications of the relativistic images are obtained using the strong deflection limit, and the results are compared with those corresponding to a Reissner-Nordström black hole with the same mass and charge. As numerical examples, the model is applied to the supermassive Galactic center black hole and to a small size black hole situated in the Galactic halo.

We present a calculation of hadron magnetic polarizability using the techniques of lattice QCD. This is carried out by introducing a uniform external magnetic field on the lattice and measuring the quadratic part of a hadron’s mass shift. The calculation is performed on a ${24}^4$ lattice with standard Wilson actions at $\mathrm{beta}=6.0$ (spacing $a=0.1\mathrm{fm}$) and pion mass down to about 500 MeV. Results are obtained for 30 particles covering the entire baryon octet ($n$, $p$, ${\Sigma }^0$, ${\Sigma }^{-}$, ${\Sigma }^{+}$, ${\Xi }^{-}$, ${\Xi }^0$, $\Lambda$) and decuplet (${\Delta }^0$, ${\Delta }^{-}$, ${\Delta }^{+}$, ${\Delta }^{++}$, ${\Sigma }^{*0}$, ${\Sigma }^{*-}$, ${\Sigma }^{*+}$, ${\Xi }^{*0}$, ${\Xi }^{*-}$, ${\Omega }^{-}$), plus selected mesons (${\pi }^0$, ${\pi }^{+}$, ${\pi }^{-}$, $K^0$, $K^{+}$, $K^{-}$, ${\rho }^0$, ${\rho }^{+}$, ${\rho }^{-}$, $K^{*0}$, $K^{*+}$, $K^{*-}$). The results are compared with available values from experiments and other theoretical calculations.

Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to the two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop axial-vector-vector (AVV) amplitude is equal to zero. According to the Vainshtein’s theorem, the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for the case of finite fermion mass in the triangle loop.

We consider QCD $t\overline{t}Z$ production at the LHC with $Z\to \overline{\nu }\nu$ and all-hadronic $t\overline{t}$ decays, i.e. $pp\to {\mathrm{p̸}}_{T}b\overline{b}+4$ jets, as a tool to measure $ttZ$ couplings. This channel has a significantly larger cross section than those where the $Z$ boson decays leptonically. However, $t\overline{t}$, $b\overline{b}+4$ jet, $t\overline{t}j$, and $t\overline{t}jj$ production give rise to potentially large backgrounds. We show that these processes can be suppressed to an acceptable level with suitable cuts, and find that adding the ${\mathrm{p̸}}_{T}b\overline{b}+4$ jet channel to the final states used in previous $ttZ$ couplings analyses will improve the sensitivity by 10%–60%. We also discuss how the measurement of the $ttZ$ couplings may constrain Little Higgs models.

A random vortex world-surface model for the infrared sector of $SU(4)$ Yang-Mills theory is constructed, focusing on the confinement properties and the behavior at the deconfinement phase transition. Although the corresponding data from lattice Yang-Mills theory can be reproduced, the model requires a more complex action and considerably more tuning than the $SU(2)$ and $SU(3)$ cases studied previously. Its predictive capabilities are accordingly reduced. This behavior has a definite physical origin, which is elucidated in detail in the present work. As the number of colors is raised in Yang-Mills theory, the corresponding infrared effective vortex description cannot indefinitely continue to rely on dynamics determined purely by vortex world-surface characteristics; additional color structures present on the vortices begin to play a role. As evidenced by the modeling effort reported here, definite signatures of this behavior appear in the case of four colors.

We discuss the experimental requirements for a mass hierarchy measurement for ${\theta }_{13}=0$ using muon-neutrino disappearance. We find that a specially optimized neutrino factory at $L\simeq 6000\mathrm{km}$ could do this measurement using extreme luminosities. In particular, we do not require charge identification for this purpose. In order to measure the mass hierarchy for more adequate luminosities, we explore the capabilities of low-energy narrow band off-axis beams, which have relatively more events at low energies. We find that, in this case, the energy resolution of the detector quickly becomes the limiting factor of the measurement and significantly affects the baseline optimization for determining the mass hierarchy.

In Witten’s open cubic bosonic string field theory and Berkovits’ superstring field theory we investigate solutions of the equations of motion with appropriate source terms, which correspond to Callan-Maldacena solution in Born-Infeld theory representing fundamental strings ending on the D-branes. The solutions are given in order by order manner, and we show some full order properties in the sense of ${\alpha }^{\prime }$ expansion. In superstring case we show that the solution is $1/2$ BPS in full order.

We present different nonperturbative calculations within the context of Migdal’s representation for the propagator and effective action of quantum particles. We calculate the exact propagators and effective actions for Dirac, scalar, and Proca fields in the presence of constant electromagnetic fields, for an even-dimensional spacetime.

The phase space of a classical particle in deformed special relativity (DSR) contains de Sitter space as the space of momenta. We start from the standard relativistic particle in five dimensions with an extra constraint and reduce it to four-dimensional DSR by imposing appropriate gauge fixing. We analyze some physical properties of the resulting theories like the equations of motion, the form of Lorentz transformations, and the issue of velocity. We also address the problem of the origin and interpretation of different bases in DSR.

We describe a possible creation of an odd number of fractionally charged fermions in the $1+1$ dimensional Abelian Higgs model. We point out that for $1+1$ dimensions this process does not violate any symmetries of the theory, nor makes it mathematically inconsistent. We construct the proper definition of the fermionic determinant in this model and outline how to generalize it for calculation of preexponent in realistic mathematically consistent $3+1$ dimensional models with the creation of an even number of fermions.

The thermodynamical properties of a dipole black ring are derived using the quasilocal formalism. We find that the dipole charge appears in the first law in the same manner as a global charge. Using the Gibbs-Duhem relation, we also provide a nontrivial check of the entropy/area relationship for the dipole ring. A preliminary study of the thermodynamic stability indicates that the neutral ring is unstable to angular fluctuations.

Recent second-order perturbation computations have provided an accurate prediction for the primordial gravitational potential, $\Phi (\mathbf{x})$, in scenarios in which cosmological perturbations are generated either during or after inflation. This enables us to make realistic predictions for a non-Gaussian part of $\Phi (\mathbf{x})$, which is generically written in momentum space as a double convolution of its Gaussian part with a suitable kernel, $f_{\mathrm{NL}}({\mathbf{k}}_1,{\mathbf{k}}_2)$. This kernel defines the amplitude and angular structure of the non-Gaussian signals and originates from the evolution of second-order perturbations after the generation of the curvature perturbation. We derive a generic formula for the cosmic microwave background angular bispectrum with arbitrary $f_{\mathrm{NL}}({\mathbf{k}}_1,{\mathbf{k}}_2)$, and examine the detectability of the primordial non-Gaussian signals from various scenarios such as single-field inflation, inhomogeneous reheating, and curvaton scenarios. Our results show that in the standard slow-roll inflation scenario the signal actually comes from the momentum-dependent part of $f_{\mathrm{NL}}({\mathbf{k}}_1,{\mathbf{k}}_2)$, and thus it is important to include the momentum dependence in the data analysis. In the other scenarios the primordial non-Gaussianity is comparable to or larger than these post-inflationary effects. We find that the Wilkinson Microwave Anisotropy Probe cannot detect non-Gaussian signals generated by these models. Numerical calculations for $l>500$ are still computationally expensive, and we are not yet able to extend our calculations to Planck’s angular resolution; however, there is an encouraging trend which shows that Planck may be able to detect these non-Gaussian signals.

We present a comprehensive study of TeV black hole events in Earth’s atmosphere originated by cosmic rays of very high energy. An advanced fortran Monte Carlo code is developed and used to simulate black hole extensive air showers from ultrahigh-energy neutrino-nucleon interactions. We investigate the characteristics of these events, compare the black hole air showers to standard model air showers, and test different theoretical and phenomenological models of black hole formation and evolution. The main features of black hole air showers are found to be independent of the model considered. No significant differences between models are likely to be observed at fluorescence telescopes and/or ground arrays. We also discuss the tau “double-bang” signature in black hole air showers. We find that the energy deposited in the second bang is too small to produce a detectable peak. Our results show that the theory of TeV-scale black holes in ultrahigh-energy cosmic rays leads to robust predictions, but the fine prints of new physics are hardly to be investigated through atmospheric black hole events in the near future.

We study the chiral symmetry restoration using the generalized hidden local symmetry which incorporates the rho and $A_1$ mesons as the gauge bosons of the generalized hidden local symmetry and the pion as the Nambu-Goldstone boson consistently with the chiral symmetry of QCD. We show that a set of parameter relations, which ensures the first and second Weinberg sum rules, is invariant under the renormalization group evolution. Then, we found that the Weinberg sum rules together with the matching of the vector and axial-vector current correlators inevitably lead to the dropping masses of both rho and $A_1$ mesons at the symmetry restoration point, and that the mass ratio as well as the mixing angle between the pion and $A_1$ meson flows into one of three fixed points.

We study pair annihilations of the neutralino dark matter in the minimal supersymmetric standard model with $CP$ violation. We consider the case that the Higgsino mass and the trilinear scalar couplings have $CP$-violating phases of order unity, taking a scenario that the scalar fermions in the first two generations are much heavier than those in the third generation to avoid a severe constraint from experimental limits on electric dipole moments. It is found that, when the lightest neutralino ($\chi$) is binolike, the cross sections of the $W$-boson pair production $\chi \chi \to W^{+}{W}^{-}$ and the lightest Higgs boson pair production $\chi \chi \to H_2^0{H}_2^0$ for nonrelativistic neutralinos can be significantly enhanced by the phase of the Higgsino mass. The relic density of the neutralino can be considerably suppressed by this effect. However, even this suppression is not enough to make binolike dark matter consistent with a cosmological constraint. We also discuss the effect of $CP$ violation on the positron flux from neutralino pair annihilations in the galactic halo.